Maximum likelihood estimation for single server queues from waiting time data (Q1357714)

The authors discuss the ML estimation of the model parameters of a \(GI/G/1\) queue based only on waiting times and derive their limit distributions. The waiting time process is Markovian with transition densities having a jump at the origin. After establishing the consistency and asymptotic normality of the ML estimators, they consider specific applications to the \(M/M/1\) and \(M/E_k/1\) queues and also present a simulation study of the \(M/M/1\) queue. The appendix contains regularity conditions and the derivation of the limiting Fischer information matrix for the \(M/M/1\) queue.